Weibull distributions have received wide ranging applications in many areas including reliability, hydrology and communication systems. Many estimation methods have been proposed for Weibull distributions. But there has not been a comprehensive comparison of these estimation methods. Most studies have focused on comparing the maximum likelihood estimation (MLE) with one of the other approaches. In this paper, we first propose an L-moment estimator for the Weibull distribution. Then, a comprehensive comparison is made of the following methods: the method of maximum likelihood estimation (MLE), the method of logarithmic moments, the percentile method, the method of moments and the method of L-moments.

Comparison of estimation methods for the Weibull distribution

In this article, we investigate various properties and methods of estimation of the Weighted Exponential distribution. Although, our main focus is on estimation (from both frequentist and Bayesian point of view) yet, the stochastic ordering, the Bonferroni and the Lorenz curves, various entropies and order statistics are derived first time for the said distribution. Different types of loss functions are considered for Bayesian estimation. Furthermore, the Bayes estimators and their respective posterior risks are computed and compared using Gibbs sampling. The different reliability characteristics including hazard function, stress and strength analysis, and mean residual life function are also derived. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation and two real data sets have been analysed for illustrative purposes.

Weighted exponential distribution: properties and different methods of estimation

This paper addresses different methods of estimation of the unknown parameters of a two-parameter Kumaraswamy distribution from a frequentist point of view. We briefly describe ten different frequentist approaches, namely, maximum likelihood estimators, moments estimators, L-moments estimators, percentile based estimators, least squares estimators, weighted least squares estimators, maximum product of spacings estimators, Cramer–von-Mises estimators, Anderson–Darling estimators and right tailed Anderson–Darling estimators. Monte Carlo simulations and two real data applications are performed to compare the performances of the estimators for both small and large samples.

Kumaraswamy distribution: different methods of estimation

A new extension of weibull distribution: Properties and different methods of estimation

The log-logistic distribution is widely used in survival analysis when the failure rate function presents a unimodal shape. Based on the log-logistic and Kumaraswamy distributions, we introduce the called Kumaraswamy-log-logistic distribution. The new distribution contains several important distributions discussed in the literature as sub-models such as the log-logistic, exponentiated log-logistic and Burr XII distributions, among several others. The beauty and importance of the new distribution lies in its ability to model non-monotonic failure rate functions, which are quite common in lifetime data analysis and reliability. Some of its structural properties are studied. We propose the Kumaraswamy-logistic regression model which has, as sub-models, various widely-known regression models. We discuss the method of maximum likelihood to estimate the model parameters and determine the observed information matrix. Two real data sets illustrate the importance and flexibility of the proposed models.

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Muna R. Alkasasbeh

Papers

Estimation of the generalized logistic distribution parameters: Comparative study